0.4 6 Repeating as a Fraction
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.46 repeating, which can be expressed as a fraction. But what is the equivalent fraction of 0.46 repeating?
What is a Repeating Decimal?
Before we dive into converting 0.46 repeating to a fraction, let's quickly review what a repeating decimal is. A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a repeating decimal because the sequence "1234" repeats indefinitely.
Converting 0.46 Repeating to a Fraction
To convert 0.46 repeating to a fraction, we can use the following steps:
Step 1: Identify the Repeating Sequence
The repeating sequence in 0.46 repeating is "46". This sequence repeats indefinitely.
Step 2: Let x = 0.46 Repeating
Let's assign x to 0.46 repeating.
Step 3: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 46.46 repeating
Step 4: Subtract x from Both Sides
Subtract x from both sides of the equation to get:
99x = 46
Step 5: Solve for x
Divide both sides of the equation by 99 to get:
x = 46/99
Therefore, 0.46 repeating is equal to 46/99.
Simplifying the Fraction
We can simplify the fraction 46/99 by dividing both the numerator and denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is:
46/99
In conclusion, 0.46 repeating can be expressed as a fraction, specifically 46/99. This equivalent fraction can be useful in various mathematical operations and applications.
